By Doron Zeilberger

Written: Dec. 7, 2005.

What is Mathematics? Most mathematicians don't know and
don't care. Mathematics is what mathematicians do.
This brilliant insight gives rise to Naturalism
(e.g. Penelope Maddy) and Humanism (or
Social Constructivism(?)) preached by Philip Davis and
Reuben Hersh.

Well, both Naturalism and Humanism seem like good ideas,
but they pertain to present day mathematics that is still
largely done by humans. In fifty years (at most) human
mathematicians will be like lamp-lighters and
ice-delivery men. All serious math will be done by
computers. Let's hope that human philosophy will still
survive, but we need to adjust naturalism to the
practice of math in the future and to the way it will
be done by machines. Of course, we don't know exactly how, so
let's put this project of Naturalist mathematical philosophy
on hold and wait to see how things turn out in fifty years.

Tim Gowers said that we are all formalists, but most of
us don't know it (and if we knew, we wouldn't care).
I kind of agree, but this is only a corollary of a more
profound truth: EVERYTHING IS COMBINATORICS.
Classify Lie Algebras? It is just root systems and
Dynkin Diagrams. Finite Groups? The Monster is
a Combinatorial Design. Even when it is not
obviously combinatorics, it could be made so.
If it is too hard for us, then we need a computer!
But computer science is all Discrete Math,
alias combinatorics. In a way Logic is too.
But Logic is so low-level, like machine language.
It is much more fun and gratifying
to work in Maple, and do higher-level combinatorics.

I am also a trivialist. Of course, I am only following
in the footsteps of King Solomon who said

ה ב ל
ה ב ל י ם
ה כ ל
ה ב ל

("hevel havalim hakol hevel"), meaning that everything
is nonsense, as well as other wise people
like Greg Chaitin and Stephen Wolfram, who realized that we humans,
and even our computers, can only prove trivial results.
Since all knowable math is ipso facto trivial, why
bother? So only do fun problems, that you
really enjoy doing.
It would be a shame to waste our short lives doing
"important" math, since whatever you can do,
would be done, very soon (if not already)
faster and better (and more elegantly!) by computers.
So we may just as well enjoy our
humble trivial work.